1. Field of the Invention
The present invention relates generally to calculating thermal stress values of materials generated under certain temperature conditions, and more particularly, to an apparatus and a method for calculating a temperature dependent Green's function using a weight function adapted to improve accuracy in the calculation of a thermal stress value by designing the weight function such that changes in physical properties of a material that change according to temperature changes are considered.
2. Description of the Related Art
In general, a Green's function is a special type of function used to solve a boundary value problem for an ordinary differential equation or an oval or parabolic partial differential equation. Green's function is named after the British mathematician George Green, who first developed the concept in the 1830s.
A technology applied using a Green's function is disclosed in Korean Patent Publication No. 2002-0041965, entitled “APPARATUS AND METHOD OF MONITORING POWER PLANT'S THERMAL STRESS”.
The following <Equation 1> represents a calculation of a thermal stress value using a Green's function.
                                                                                          σ                  Γ                                ⁡                                  (                                      p                    ,                    t                                    )                                            =                                                ∫                                      t                    -                                          t                      d                                                                      ⁢                                                      G                    ⁡                                          (                                              p                        ,                                                  t                          -                          τ                                                                    )                                                        ⁢                                      ∂                                          ∂                      τ                                                        ⁢                                      ϕ                    ⁡                                          (                      τ                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    τ                                                                                                                          =                                                                                          G                      s                                        ⁡                                          (                      p                      )                                                        ⁢                                      ϕ                    ⁡                                          (                      t                      )                                                                      +                                                      ∑                                          t                      -                                              t                        d                                                              t                                    ⁢                                                            G                      ⁡                                              (                                                  p                          ,                                                      t                            -                            τ                                                                          )                                                              ⁢                    Δ                    ⁢                                                                                  ⁢                                          ϕ                      ⁡                                              (                        τ                        )                                                                                                                                                    <                  Equation          ⁢                                          ⁢          1                >            
where Gs(p) represents a Green's function at a predetermined point after an attenuation period elapses, and φ(τ) represents an actual temperature measurement value at a monitoring position that is changed over time. G(p,t−τ) is a Green's function during an attenuation period, and Δφ(τ) represents a temperature change value during an attenuation period at a predetermined interval.
Accordingly, since Gs(p) and G(p,t−τ) are predetermined values, thermal stress a σΓ(p,t) is determined by φ(t) and Δφ(τ), which are actual temperature measurement values at a monitoring position that is changed over time.
Additionally, a thermal stress value at an arbitrary time and position is obtained by multiplying a differential value of a boundary temperature to a Green's function and then integrating its result for a given time.
Meanwhile, since changes in thermal, mechanical and physical properties (for example, thermal conductivity coefficient, thermal expansion coefficient, specific heat coefficient, and elastic coefficient) of materials changed depending on temperature change ultimately change thermal stress values of materials, changes in physical properties of materials depending on temperature change must be considered. However, an existing Green's function does not reflect such changes and thus cannot obtain accurate thermal stress values.